Line Spectrum of Hydrogen

An emission spectrum shows the wavelengths emitted by a substance after absorbing energy, with excited atoms releasing energy as they return to a lower state. This results in a line spectrum in gases, where specific wavelengths appear as bright lines separated by dark gaps unique to each element. Conversely, an absorption spectrum occurs when a substance absorbs specific wavelengths from a continuous spectrum, creating dark lines at the absorbed wavelengths.

1.0Spectral Emission

Spectral Emission occurs when an electron moves from a higher energy level (n₂) to a lower energy level (n₁). This transition releases energy as a photon, with the photon's energy corresponding to the difference between the two energy states. Since the energy levels of an atom are quantised and fixed, the emitted photon will always have the same energy for a given transition. This leads to a spectrum with specific wavelengths that reflect the differences between the energy levels in the atom.

2.0Spectral Series of Hydrogen

As the simplest atomic system, the hydrogen atom exhibits the most straightforward spectral series. When a beam of light or radiation passes through a slit and is observed using a spectroscope, it creates a series of images that appear as parallel lines. These lines are arranged side-by-side with uniform spacing, representing individual components of the radiation. As one moves from higher to lower wavelengths, the spectral lines are more widely spaced on the high-wavelength side and progressively closer together on the low-wavelength side. The shortest wavelength, the series limit, features the most closely packed spectral lines.

In 1885, Johann Jakob Balmer, a Swedish teacher, first identified a series in the visible region of the hydrogen spectrum known as the Balmer series. This series corresponds to electron transitions from higher energy levels to the second energy level (shell).

Other notable hydrogen spectral series include:

Lyman Series: Electron transitions to the first energy level from any higher level.
Balmer Series: Electron transitions to the second energy level from any higher level.
Paschen Series: Electron transitions to the third energy level from any higher level.
Bracket Series: Electron transitions to the fourth energy level from any higher level.
Pfund Series: Electron transitions to the fifth energy level from any higher level.

Each series corresponds to specific regions of the electromagnetic spectrum, ranging from ultraviolet (Lyman) to infrared (Paschen, Bracket, and Pfund).

Spectral Series	Spectral Region	n₁	n₂	Wavelength (Å)
Lyman Series	Ultraviolet	1	2, 3, 4, 5, 6, 7, …..	920 - 1200
Balmer Series	Visible light	2	3, 4, 5, 6, 7, ...	4000 - 6500
Paschen Series	Infrared	3	4, 5, 6, 7, ...	9500 - 18750
Brackett Series	Infrared	4	5, 6, 7, ...	19450 - 40500
Pfund Series	Infrared	5	6, 7, ...	37800 - 75000
Humphrey Series	Infrared	6	7, ...	>75000

When an electric discharge is applied to gaseous hydrogen, the H₂ molecules break apart, forming excited hydrogen atoms. These excited atoms emit electromagnetic radiation at specific, discrete frequencies, leading to the hydrogen emission spectrum, which consists of several spectral lines named after its discoverers.

In 1885, Johann Balmer observed that the visible lines in the hydrogen spectrum could be described using a mathematical formula. When expressed in terms of wavenumber

( $\overset{ν}{ˉ}$ ), these lines follow:

$\overset{ν}{ˉ} = R_{H}$ $(\frac{1}{2 ^{2}}$ - $\frac{1}{n ^{2}})$

where:

R_H is the Rydberg constant,
n is an integer equal to or greater than 3 (i.e., n = 3,4,5,……).

This equation specifically applies to the Balmer series, which corresponds to the visible region of the hydrogen spectrum.